sharkdp/numbat

Numbat has a static type system where physical dimensions like Length and Time act as types. Definitions of constants and functions can optionally contain type annotations that will be statically enforced. If the types are not specified, they will be inferred (Speed, Money and Frequency in the screenshot).

See this article to learn more about Numbat's type system.

Numbat is focused on computations with units. Units are therefore treated as first-class citizens. They can be entered in various ways (km/h or kilometer/hour, GiB or gibibytes, ° or degree, m² or m^2). New units can be introduced on the spot (unit pixel). Compatible units can be converted easily using the -> operator (30 km/h -> mph, 1 mrad -> degree, 5 in + 2 ft -> cm, 27 weeks -> days). And unit expressions are simplified using various heuristics (15 km/h * 30 min = 7.5 km).

Numbat's standard library comes with a large number of physical dimensions and units (SI, US Customary, Imperial, Nautical, Astronomical, Atomic, Nuclear, …). See this reference page for a complete overview. It also contains a lot of mathematical and physical constants as well as a large range of pre-defined functions.

Numbat's parser never tries to be "smart" on syntactically incorrect input. This means you will either get a (descriptive) error message, or you can trust the result of your calculation.

Numbat aims to provide descriptive and helpful error messages.

Numbat has been designed for an interactive use-case with small "one off" computations. Opening the numbat interpreter without any arguments starts a REPL with a familiar readline interface, including all the usual features like a command history, Ctrl-R search or tab completion.

The whole system of physical dimensions and units is specified Numbat's standard library, which is written in the Numbat language itself. It is therefore easily extensible by providing a init.nbt file. For example, a single line (unit bathtub = 150 L) is usually enough to add a new unit. Users can even choose to write their own prelude module, allowing for arbitrary modifications to the unit system.

With its static type system, Numbat already enforces correctness of your calculations on a physical dimension level. But some checks can only be made at runtime. Numbat provides an assert_eq procedure that allows you to check for exact equality using assert_eq(12 ft, 1 in) or approximate equality using assert_eq(c, 300_000 km/s, 1% × c). This can be useful to make sure that intermediate results do not change during a restructuring of your calculation.

Numbat is a scientific calculator. It's not a computer algebra system that solves differential equations or computes intergrals. Try WolframAlpha instead.
There is no graphical user interface with buttons like x², 1/x or DEG/RAD. Qalculate! is a fantastic tool that supports both text as well as graphical input.
Numbat supports a huge range of physical units. If you need something even more comprehensive, please consider contributing. Or try GNU units.